This really hits home for me. My exh and I both started to develop emotionally intimate relationships and we agreed to have a don't ask don't tell (mistake)... Things worked really well for a while. Probably the happiest I have been. Unfortunately, I think my feelings fell more deep in this and he was more on the spectrum of his partner being a good time. Now, post divorce, I had to challenge him that me being the person who consoled her through vague mental breakdowns when he started to pull back that there was emotional intimacy there for her. She was my close friend and I guess I was okay with the blurring of boundaries because I felt like they both cared about me... Eventually he wanted to go back to being a normal married couple and asked me a lot about my other relationship. He asked, I told... And from there, he wanted it to end... And he created a fantasy where things just go back to how they were...
I really struggle with the lack of choice, because my heart was tied to my other partner. Eventually, my exh and I split because of many reasons, but definitely some contributing factors were my continuing connection to this other person and also not enough space/time to heal our own connection...
Fast forward, my other connection's partner pushed our connection a lot when she didn't want a romantic relationship with him, and was okay for years with us being close, going to events together, etc. When I became ''single", she became threatened by our connection, and after a rollercoaster of no, yes, no, yes defaulted to the same stance. I don't care what happened in the past, but it needs to stop now. Unfortunately for me, he tried to play both sides for a bit, under the confusion card, and dragged my heart through the mud, until eventually things were make or break on his end, and I was the piece that didn't fit.
My point is, I became collateral damage in this and the impact was devastating for me. I respect people's right to choose what works for them and what doesn't, but your wife allowed you to open the door and then expected you to close it on her command. For me, it felt very unfair to be allowed to develop this connection only to be penalized for its existence years later. I learned a lot of hard lessons through this experience, but it made me acutely aware that opening up a relationship shouldn't be taken lightly. I think if a couple is going down this route, they really need to think about how to handle a situation like this, because real people are tied into these decisions. Don't be careless with curiosity.
I don't have much advice other than I trust if you are being forced to do something that you don't want to do it to appease another person, that long term it's going to lead to other issues. It has to be your decision. And your decision can be "I am willing to sacrifice this relationship to make it work for my wife." But if that isn't your decision, then the conversation with your wife that this is something that is a part of your life now, and you want her to be too, what can you guys do to increase her comfort and security to know you are here with her too?